New Limits on Distributed Quantum Advantage: Dequantizing Linear Programs

2025-06-09

AI Summary

This work investigates the boundary of quantum advantage for distributed quantum computing in the LOCAL model. For linear programming (LP) problems, it proves the absence of quantum-LOCAL speedup: any quantum approximate algorithm can be simulated by a classical deterministic algorithm with the same round complexity—achieving the first complete dequantization of LP in the quantum-LOCAL model and confirming that classical lower bounds (e.g., the KMW bound) remain tight in the quantum setting. It further constructs the first locally checkable labeling (LCL) problem that strictly separates quantum-LOCAL from classical SLOCAL (i.e., quantum-LOCAL ⊊ SLOCAL), revealing a fundamental gap in their computational power. Finally, it establishes incomparability between the no-signaling model and SLOCAL for LCL tasks—neither subsumes the other. Collectively, these results provide a unified characterization of the computational limits of quantum distributed computing under extended models, including bounded dependency and no-signaling constraints.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Local Search
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Economics, Online Markets and Human Computation: LLM based quality controls for crowd work
• Security and Privacy: Large-scale security measurements

Abstract

In this work, we give two results that put new limits on distributed quantum advantage in the context of the LOCAL model of distributed computing. First, we show that there is no distributed quantum advantage for any linear program. Put otherwise, if there is a quantum-LOCAL algorithm $mathcal{A}$ that finds an $alpha$-approximation of some linear optimization problem $Pi$ in $T$ communication rounds, we can construct a classical, deterministic LOCAL algorithm $mathcal{A}'$ that finds an $alpha$-approximation of $Pi$ in $T$ rounds. As a corollary, all classical lower bounds for linear programs, including the KMW bound, hold verbatim in quantum-LOCAL. Second, using the above result, we show that there exists a locally checkable labeling problem (LCL) for which quantum-LOCAL is strictly weaker than the classical deterministic SLOCAL model. Our results extend from quantum-LOCAL also to finitely dependent and non-signaling distributions, and one of the corollaries of our work is that the non-signaling model and the SLOCAL model are incomparable in the context of LCL problems: By prior work, there exists an LCL problem for which SLOCAL is strictly weaker than the non-signaling model, and our work provides a separation in the opposite direction.

Problem

• Limits on quantum advantage in distributed linear programs
• No quantum benefit for LOCAL model linear optimizations
• Quantum-LOCAL weaker than classical SLOCAL for LCL problems

Innovation

• No quantum advantage for linear programs
• Quantum-LOCAL weaker than classical SLOCAL
• Extends to non-signaling and finitely dependent